feat(web): mode-aware backlog banner — stop telling manual users summaries auto-arrive

The first pilot user sat in Manual mode reading "new summaries land gradually,
check back tomorrow" — copy that only makes sense in Automatic mode. Manual mode
never auto-summarizes, so the banner promised delivery that would never come.

The list page now reads the user's summarize mode and shows mode-correct copy:
- Auto: unchanged "land gradually" backlog note.
- Manual: "new videos appear here but are not summarized automatically — use the
  Summarize button" plus a "Switch to Automatic" link to /account.
The connected-but-empty first-run state is likewise mode-aware.

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

internal/web/paste_test.go

@@ -65,7 +65,7 @@ func TestParseYouTubeVideoID(t *testing.T) {
 func TestListPageShowsPasteFormOnlyWhenConnected(t *testing.T) {
 	render := func(connected bool) string {
 		var buf bytes.Buffer
-		if err := ListPage(listBuckets{}, Filter{}, PipelineStats{}, "", connected, nil).Render(context.Background(), &buf); err != nil {
+		if err := ListPage(listBuckets{}, Filter{}, PipelineStats{}, "", connected, nil, true).Render(context.Background(), &buf); err != nil {
 			t.Fatalf("render: %v", err)
 		}
 		return buf.String()